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URL: https://oeis.org/A364266

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A364266
The first term in a chain of at least 3 consecutive numbers each with exactly 5 distinct prime factors.
8
1042404, 3460280, 3818828, 3998664, 4638984, 4991964, 5540248, 5701254, 5715500, 5964958, 6772050, 6794084, 7237384, 7453964, 7459088, 7745318, 7757034, 7993194, 8083634, 8153430, 8168194, 8273628, 8340834, 8340980, 8414756, 8486994, 8698898, 8722634, 8758904
OFFSET
1,1
LINKS
FORMULA
a(1) = A087978(3).
{k: A001221(k) = A001221(k+1) = A001221(k+2) = 5}. - R. J. Mathar, Jul 18 2023
EXAMPLE
1042404 = 2^2*3*11*53*149, 1042405 = 5*6*143*29*79 and 1042406 = 2*17*23*31*43 each have 5 distinct prime factors, so 1042404 is in the sequence.
MAPLE
omega := proc(n)
nops(numtheory[factorset](n)) ;
end proc:
for k from 1 do
if omega(k) = 5 then
if omega(k+1) = 5 then
if omega(k+2) = 5 then
print(k) ;
end if;
end if;
end if;
end do:
MATHEMATICA
seq[lim_] := Module[{s = {}, q1 = False, q2 = False, q3}, Do[q3 = PrimeNu[k] == 5; If[q1 && q2 && q3, AppendTo[s, k-2]]; q1 = q2; q2 = q3, {k, 3, lim}]; s]; seq[10^7] (* Amiram Eldar, Oct 01 2024 *)
CROSSREFS
Cf. A192203 (subsequence for squarefree triples). Subsequence of A140079 (2 consec.) and of A006073.
Cf. A364308 (3 dist. factors), A364309 (4 dist. factors), A364265 (6 dist. factors), A001221, A087978.
Sequence in context: A030084 A030092 A237073 * A179448 A289825 A013696
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jul 16 2023
STATUS
approved